In [1]} Segal studied the related
notion of a good simplicial space: this was a simplicial
space \(X\)  for which all the degeneracy
maps were closed cofibrations. Both the
notion of proper and the notion of good make sense
in the setting of a bicomplete topological
category \({C}\) . We say (in analogy with
Definition 22.4.2 of [2]}) that a simplicial object \(X\)  in \(s{C}\)  is
proper if the latching maps \(L_nX\rightarrow X_n\)  are
\(\bar{h}\) -cofibrations for all \(n\ge 0\) .
Similarly we say that \(X\)  is good if all of the degeneracy morphisms
\(s_i\colon X_n\rightarrow X_{n+1}\)  are all \(\bar{h}\) -cofibrations.
